Entropy, Landscapes, and Fragility in Liquids and Polymers, and the ΔCp Problem

We examine the relation of the mode coupling theory of glassforming liquid dynamics to the Gibbs-Goldstein landscape picture of relaxation, and identify, using both scaling relationships and thermodynamic calculations, where the crossover between the two domains occurs. This "landscape" approach is then applied to chain polymers, using a neglected relation between the WLF C₁ parameter and the high frequency limit for relaxation, to establish the characteristic temperature of the landscape ground state and the appropriate fragility parameters. A problem with the relation between thermodynamic to relaxational assessments of the landscape "height" is used to focus attention on a problem with the heat capacity changes at T_g in the case of chain polymer melts and their glasses.